The present invention relates to a transmit filter for high-bit-rate digital subscriber line (HDSL2 systems). The HDSL2 standard (currently, Draft HDSL2 Standard, T1E1. 4/2000-006, ANSI) requires both the upstream and the downstream transmitted power spectrum densities (PSDs) to be below a certain level. Such transmitted power specifications are standard on present and future communication systems. It is desired to have a transmit power that comes close to but does not exceed the maximum allowable power at any frequency. Because the specification is relatively complex, it is difficult to come up with a low-order filter that allows the system to approach the maximum allowed power output.
Additionally, transmit filters which are produced using conventional methods to approach the maximum PSDs for the different frequencies of the HDSL2 specification tend to be quite complex having coefficients into the hundreds. This becomes quite difficult to implement in a realistic system. Typically, less accurate lower-order filters are used, giving up some of the allowed power spectrum density at certain frequencies.
It is desired to have an improved transmit filter and method for calculating transmit filter coefficients.
This invention describes a two-step procedure for the design of transmit filter for the communication system with maximum allowable power spectral density. First, the relevant section of the transmit path is partitioned into two parts: (i) the transmit filter that needs to be designed, and ii) the remaining elements that affect the output but not part of the transmit filter, modeled as a fixed weighting function. In contrast to conventional approaches, in one embodiment of the present invention, the transmit filter is selected by optimizing the autocorrelation coefficients via convex optimization methods, and then extracting filter coefficients from autocorrelation coefficients. The structure of the convez optimization allows for a Linear Programming (LP) solution. In the system of the present invention, transmit filter with thirty-two coefficients provides a power spectral density close to the maximum allowed.